The radius of the circle with the same vertex is 6 and the height of the triangle is 10.39 and the area of the triangle is 62.34.
Since the arc divides the triangle into two regions of equal area, it follows that half of the circle's area is equal to the area of the triangle. The area of a triangle with sides 12 and 12√3 and a 60-degree angle can be found using the formula for the area of a triangle, which is 0.5bh.
The height of the triangle can be found using trigonometry, as the sine of 60 degrees is 0.8660. Thus, the height of the triangle is 10.39 and the area of the triangle is 62.34.
Since half of the circle's area is equal to the area of the triangle, the radius of the circle can be found by taking the square root of the area of the triangle and dividing it by pi. Thus, the radius of the circle is 6.
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A triangle has a 60-degree angle, and the two adjacent ide are 12 and 12 roots 3. Find the radius of a circle with the same vertex a center, if the arc inside the triangle divides it into two regions of equal area
To find the roots of a polynomial, it is often useful to find the ____ of the polynomial.
Answer:
factors
Step-by-step explanation:
To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.
frustrated freight may never reach the intended recipient T/F
True, Frustrated Freight is any freight or shipment that it has been halted from moving.
Generally speaking, the elements that make a bundle quit moving or being shipped to the normal beneficiary are issues to do with marking, bundling, as well as making.
Frustrated Freight alludes to products that can't be conveyed to the expected beneficiary because of different reasons like an erroneous location, beneficiary inaccessibility, or harm during travel.
This can prompt the shipment never arrive at its expected objective, causing disillusionment for the shipper and beneficiary, and possibly bringing about monetary misfortunes.
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Gayle bought a shirt that was originally marked as $18. She had a coupon to receive 15% off the price. Gayle
had to pay 7. 5% sales tax on her shirt. What price did Gayle pay for the shirt?
sssssssssaStep-by-step explanation:
Evaluate lim f(x) and lim f(x) for the following function. Use co or co where appropriate. Then give the horizontal asymptote(s) of f (if any).
f(x)= 3x^3+8/4x^3+√ 64x^64
The limit of f(x) as x approaches positive infinity and negative infinity is equal to 3/4, and the horizontal asymptote of the function is y=3/4.
The horizontal asymptote of a function is a horizontal line that the function approaches as x approaches infinity or negative infinity.
The function f(x) is given by
=> f(x)= 3x³ + 8/4x³ + √ 64x⁶⁴.
To evaluate the limits, we need to consider what happens as x approaches positive infinity and negative infinity.
In this case, as x approaches positive infinity or negative infinity, the x³ term in the numerator and denominator will dominate and the limit of the function will be equal to 3/4.
This means that the function has a horizontal asymptote of y=3/4.
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a woman has two kids, one of which is a girl. what is the probability of the other child being a girl?
The probability of the other child being a girl is 1/2
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
Kids = 2
Girls = 1
The probability of the other child being a girl is calculated as
Probability = Girl/Kids
Substitute the known values in the above equation, so, we have the following representation
Probability = 1/2
Hence, the probability is 1/2
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Elijah spends $6.65 at the concession stand. He paid with a $10 bill. How much
change did Elijah get back?
Elijah received $ in change.
Answer:$3.35
subtract 10.00 - 6.65
You will get $3.35
The equation s equals three fourths times f represents the proportional relationship between the amount of sugar (s) and flour (f) in a recipe. Which table represents the equation of the proportional relationship?
Sugar Flour
1 six fourths
2 three fourths
Sugar Flour
six fourths 1
three fourths 2
Sugar Flour
three fourths 1
six fourths 2
Sugar Flour
1 three fourths
2 six fourths
The table that represents the equation of the proportional relationship is; Table 4
How to find the proportional relationship?A proportional relationship is defined as a mathematical relationship that exists between two variables in which their ratio is always equal.
We have that the equation s equals three fourths times f. This is expressed as;
s = ³/₄f
where;
s is the amount of sugar
f is the amount of flour
Table 1;
when f = 1
s = ³/₄(1)
s = ³/₄
when f = 2
s = ³/₄(2)
s = 6/4
Thus, table 4 is correct
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How do you convert acres to miles?
The convert acres to miles 0.0015625.
What is meant by miles ?
The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 metres, establishing a standard between the British Commonwealth and the United States.The Romans split a mile into 5,000 Roman feet, but in Elizabethan England, where furlongs were valued more highly, the statute mile was changed in 1593 to be equal to 8 furlongs, or 5,280 feet.To learn more about miles refer to
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use the general slicing mothod to find the volume of the following solid. The solid with a semicircular base of radius 9 whose cross section is perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.
The volume of the solid is approximately equal to 441.75 π cubic units.
The volume of the solid can be found using the disk method of integration. To set up the integral, consider a disk of height 'h' and radius 'r' at position y. The volume of this disk is given by πr^2h, and the radius 'r' is equal to 9 - y. Therefore, the volume of the solid is given by the following triple integral:
[tex]V = \int\{\pi(9 - y)^2dy} \int\,dh \int\,dx[/tex]
Where the limits of integration are:
For x: 0 to 9 (since the square cross-section has side length of 9)For h: 0 to x (since the height of the disk cannot be greater than the distance from the xy-plane)For y: 0 to 9 (since the radius of the semicircle is 9)So, the final expression for the volume is:
[tex]V = \int\limits^{9}_{y=0} \int\limits^{x}_{h=0} \int\limits^{9}_{x=0} \pi (9 - y)^2 dh dx dy[/tex]
Evaluating the integral gives:
[tex]V = \pi \int\limits_{y=0}^{9} (9 - y)^2dy \int\limits_{h=0}^{x} dh \int\limits_{x=0}^{9} dx[/tex]
[tex]= \pi \int\limits_{y=0}^{9} (81 - 18y + y^2)dy \int\limits_{h=0}^{x} dh \int\limits_{x=0}^{9} dx[/tex]
[tex]= \pi \int\limits_{y=0}^{9} (81 - 18y + y^2)dy (x^2/2) dx[/tex]
[tex]= \pi /2 \int\limits_{y=0}^{9} (81 - 18y + y^2)dy (x^2) dx[/tex]
[tex]= 441.75 \pi[/tex]
Hence, the volume of the solid is approximately equal to 441.75 π cubic units.
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. if v in r 3 and v · v = 0, then v is the zero vector. is it true or false? explain your answer
The statement "if v in R3 and v · v = 0, then v is the zero vector" is true
In mathematics, a vector is an ordered tuple of numbers or scalars that can be used to represent a quantity that has both magnitude and direction. Vectors are used to model physical quantities such as displacement, velocity, and force, among others.
Here we have given that if v in r 3 and v · v = 0, then v is the zero vector.
It is true because if the dot product of a vector with itself is zero, it means that the magnitude of the vector is zero and thus it is the zero vector. Understanding the concept of a zero vector and its relationship with other vectors is important in mathematics and physics.
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How do you know if results are practically significant?
In order to determine the practical significance requires considering both the effect size measures and the context of the study
One way to determine practical significance is by using effect size measures. Effect size is a standardized measurement of the magnitude of a treatment or intervention.
A common equation used to calculate effect size is Cohen's d, which is the difference between the means of two groups divided by the standard deviation.
Another equation used is the odds ratio, which is the ratio of the odds of an event occurring in one group compared to another.
Additionally, it is important to consider the context of the study when evaluating practical significance.
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Here are graphs of three exponential equations.
Match each equation with its graph.
6,000
4,000
2,000
Column A
1.
2
3
-
f(x) = 100 (3)^x
g(x) = 100 (35)^x
h(x) = 100 (4)^x
B
U
3
Column B
a. C
b. A
C. B
Answer:
f(x) = 100 (3)^x <===> C
f(x) = 100 (3.5)^x <===> B
f(x) = 100 (4)^x <===> A
Step-by-step explanation:
Since the base of each of the exponential functions is the same, the higher the base, the higher up the graph will be with respect to another base with a lower value
This can be easily determined by choosing a specific value for x for each equation and seeing what the f(x) value is
Let's choose x = 2
For f(x) = 100 (3)^x, at x = 2 we get f(2) = 100(3)^2 = 100 x 9 = 900
For f(x) = 100 (3.5)^x, at x = 2 we get f(2) = 100(3.5)^2 = 100 x 12.25 = 12.25
For f(x) = 100 (4)^x, at x = 2 we get f(2) = 100(4)^2 = 100 x 16 = 1600
So for a specific value of x, the higher the base, the higher the graph is relative to the x-axis
So the matches are:
f(x) = 100 (3)^x <===> C
f(x) = 100 (3.5)^x <===> B
f(x) = 100 (4)^x <===> A
Solve the absolute value equation for x. |4 − 2x| + 6 = 18 Enter your answers in the blanks in order from least to greatest. x=□ or □
The solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:
x = -4 or x = 8
What is inequality?
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.
We can solve this absolute value equation by first isolating the absolute value term on one side of the equation and then solving for both possible cases. Here are the steps:
|4 − 2x| + 6 = 18
|4 − 2x| = 12 (subtract 6 from both sides)
Now we have an absolute value equation with no constant term. We can split this equation into two cases: one where the expression inside the absolute value is positive, and one where it is negative. For each case, we can solve for x:
Case 1: 4 - 2x > 0
If 4 - 2x is positive, then we can drop the absolute value bars and write:
4 - 2x = 12
-2x = 8
x = -4
So one solution is x = -4.
Case 2: 4 - 2x < 0
If 4 - 2x is negative, then we must flip the inequality when dropping the absolute value bars:
-(4 - 2x) = 12
-4 + 2x = 12
2x = 16
x = 8
So the other solution is x = 8.
Therefore, the solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:
x = -4 or x = 8
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Please help me with math problem!! Will give brainliest!! :) It's due tonight!! 20 POINTS!!!
Answer:
[tex]\boxed{21.691} \; feet[/tex]
Step-by-step explanation:
See attached figure
The power cable going south first by 50 feet and then going west by 30 feet form the legs of a right triangle.
The diagonal which is the shortest distance between start and end points can be computed by the Pythagorean theorem
[tex]c^2 = a^2 + b^2[/tex]
where c is the hypotenuse and a, b the other two sides
Plugging in values for a = 50 and b = 30 we get
[tex]c^2 = 50^2 + 30^2\\\\c^2 = 2500 + 900\\\\c^2 = 3400\\\\c = \sqrt{3400}\\\\c = 58.3095 \;feet[/tex]
The cable length if going south and then west will be 50 + 30 = 80 feet
So cable length saved = 80 - 58.3095 = 21.6905
Rounded to 3 decimal places this would be 21.691 feet
Answer:
By using the Pythagorean Theorem, we can calculate that the diagonal of the city block is approximately 58.3 feet long. This means that the power company could save 7.3 feet of powerline cable by running the powerlines across the diagonal of the city block, instead of around the south and west sides.
Kevin was solving for the area of the triangle below.
The formula for area of a triangle is A = bh. Kevin's answer
for the area of this triangle was 40 inches².
Is Kevin's solution correct? Why or why not?
If not, what was his mistake?
If not, what is the correct solution for the area of this
triangle?
Kelvin's solution is correct because he multiplies the base of the triangle by the height of the triangle.
What is the area of the triangle?Area of triangle= base × height
The base of the triangle= 5 in
The height of the triangle = 8 in
Area of triangle= base × height
= 5 in × 8 in
= 40 square inches
Consequently, the area of the triangle as calculated by kelvin is correct.
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In a certain species of plant, the color purple (p) is dominant to the color white (p). According to the punnett square, what is the probability of an offspring being white?.
Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.
what is the probability of an offspring being white?.Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.
It is used to know the result of the genotype of the offspring having either having single or multiple traits.
The correct answers are:
1.Option C. 0%
In the Punnett square the cross is between the purebred dominant and purebred recessive parent.
This will result in all the offspring having a heterogeneous genotype trait carrying purple color. Hence 0% will carry white color.
2. Option D. 25%
It can be explained as:
Due to the presence of heterogenous parent species. It will result in 25% of offspring carrying white color.
Therefore, in question 1, 0% of plants will be white while in another question 25% of the offspring will carry the white color trait.
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given the linear system y[n] = 0.25y[n-1] x[n] for n > 0 and y[-1]=0 system is described by the impulse response h[n] = [0.25]nu[n]. determine if the system is stable or not
The system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.
The stability of a linear system can be determined by analyzing the magnitude of its impulse response −
|h[n]| ≤ M for some finite M
In this case, the impulse response is h[n] = 0.25nu[n], where nu[n] is the unit step function. Since the magnitude of h[n] is 0.25 for all n, the system is stable since 0.25 is a finite number that is less than any M.
To summarize, the system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.
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The surface area of a sphere is 544 cm². Find its diameter. Take π= 22/7 (Give your answer correct to 1 decimal place)
Answer:
13.2cm
Step-by-step explanation:
The surface area of the sphere=4πr∧2
take r as radius, so you have to find the diameter. which means d/2=r
So,
4*22/7* (d/2)²=544
d=13.15
to the first decimal place= d= 13.2 cm.
Select all equations that have x = 9 as a solution.
Check all that are true.
x + 7 = 15
26 − x = 17
5x = 49
63 ÷ x = 7
23 + x = 32
for each of the statements below, give a domain of discourse for which the statement is true, and a domain for which the statement is false. (a) ∀x∃y(y 2 x). (b) ∀x∀y(x < y → ∃z(x < z < y)
A domain of discourse for a domain integer statement is,
(a) True : x ≥ 0 and False x < 0
(b) True : x ≠ z ≠ y and False x ≠ y = z
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
An integer, also called a "round number" or “whole number,” is any positive or negative number that does not include decimal parts or fractions. For example, 3, -10, and 1,025 are all integers, but 2.76 (decimal), 1.5 (decimal), and 3 ½ (fraction) are not.
(a) ∀x∃y( [tex]y^{2}[/tex] ≥ x)
[tex]y^{2}[/tex] ≥ 0
When x ≥ 0 , [tex]y^{2}[/tex] = x is True.
When x < 0 , without [tex]y^{2}[/tex] = x is True.
(b) ∀x∀y(x < y → ∃z(x < z < y)
When x ≠ z ≠ y , x < z < y is True.
When z = x or z = y , x < z < y is False.
When x = y and x = z , y = z
Therefore,
A domain of discourse for a domain integer statement is,
(a) True : x ≥ 0 and False x < 0
(b) True : x ≠ z ≠ y and False x ≠ y = z
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A city currently ha 132 treetlight. A part of an urban renewal program, the city council ha decided to intall 4 additional treetlight at the end of each week for the next 52 week. Ue thi information to complete the following tatement. Round to the nearet whole number a needed. The city will have (blank) treetlight at the end of 46 week. The city will have 232 treetlight at the end of (blank) week
They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
At the end of 46 week the city will have: 132 streetlight + (4 streetlight/ week * 46 weeks)
At the end of 46 week the city will have: 132 streetlight + 184 streetlight
At the end of 46 week the city will have: 316 streetlight
232 streetlight at the end of the week = (232 streetlight - 132 streetlight) / 4 streetlight /week
232 streetlight at the end of the week = 100 streetlight /4 streetlight /week
232 streetlight at the end of the week = 25 weeks
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Correctly written question:
A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed. The city will have (blank) streetlights at the end of 46 weeks. The city will have 232 streetlights at the end of (blank) week
:(help pleaseeeeeeeeeee
The values of the letters are:
A = $37.5
B = $16.95
C = 5
D = $15.34
How to determine the values of the letter?A sales tax is a tax paid to the government for the sales of certain goods and services.
Total price = Quantity * Unit Price
Unit price = Total price / Quantity
Quantity = Total price / Unit price
A = Total price = 3 * 12.5 = $37.5
B = Unit price = 33.90 / 2 = $16.95
C = Quantity = 31.00 / 6.20 = 5
15% VAT = 15% of Total Price
D = 15/100 * 108.28 = $15.34
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Let u = 26 [ 4 -2] and A= -5 9 . Is u in the plane in R3 spanned by the columns of A? Why or why not? 1 1 Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) O A. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. O B. No, the reduced row echelon form of the augmented matrix is , which is an inconsistent system
No, u is not in the plane spanned by the columns of A.
To check if u is in the plane spanned by the columns of A, we first need to construct the augmented matrix of the system A · x = u, where x is the vector of unknowns. The augmented matrix is:
[−5 9 | 26 4 −2]
The reduced row echelon form of this augmented matrix is:
[1 0 | 2 -1]
This is an inconsistent system,the reduced row echelon form of the augmented matrix is , which is an inconsistent system so it does not have any solutions. This means that u cannot be written as a linear combination of the columns of A, so it is not in the plane spanned by the columns of A.
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Suppose that the data y = (y1,..., yn) are a sample from a normal distribution with unknown
mean θ and known standard deviation σ = 2. Our prior distribution p(θ) is normal with mean
0 and standard deviation σ0.
(a) For an uninformative prior, do we need a large or small value for σ0? [2]
(b) We want the prior probability P(|θ| ≤ A+10) to be 0.95, where A is the third-to-last digit
of your ID number. What value for σ0 should we choose? [4]
(c) A colleague prefers a Cauchy distribution as a prior. What is a possible reason for this
preference?
the data y = (y1,..., yn) are a sample from a normal distribution with unknown mean θ and known standard deviation σ = 2. Our prior distribution p(θ) is normal with mean 0 and standard deviation σ0.
y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1 y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1
We have two cases for Ф,
1. Ф=1; it implies that Pr(Ф=1)=0.5, while y~N(1,α²)
2. Ф=2; it implies that Pr(Ф=2)=0.5, while y~N(2,α²)
Now,
For 1st case of α=2,
We have marginal probability density formula
p(y)=∑p(yIФ)p(Ф)
=p(yIФ=1)p(Ф=1)+p(yIФ=2)p(Ф=2)
=N(yI1,2²)(1/2)+N(yI2,2²)(1/2)
=(1/2)[N(yI1,2²)+N(yI2,2²)]
Now.
For Pr(Ф=1Iy=1) at α=2
We have,
=p(Ф=1Iy=1)
=[p(y=1,Ф=1)]/[p(y=1)]
=[p(y=1IФ=1)p(Ф=1)]/[p(y=1)]
={(1/)exp[(-1/(2*2²))(1-1)²(1/2)]}/{(1/)(1/2)[exp[(-1/(2*2²))(1-1)²]+exp[(-1/(2*2²))(1-2)²]}
=0.53 Answer
Now, to describe the changes in shape of Ф when α is increased and decreased deviation
The formula for posterioir density is p(ФIy)=p(yIФ)p(Ф)/p(y)
=exp[(-1/(2α²)(y-Ф)²]/{exp[(-1/(2α²)(y-1)²]+exp[(-1/(2α²))(y-2)²]}
Now at Ф=1 and solving the equation, we get
p(Ф=1Iy)=1 / {1+exp[(2y-3)/2α²]}
Similarly at Ф=1 and solving the equation, we get
p(Ф=2Iy)=1 / {1+exp[(2y-3)/2α²]}
Conclusion:
α² → ∞ ⇒p(ФIy) → p(Ф) = 1/2
α² → 0 ⇒ two cases
y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1
y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1
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What are the 6 Laws of logarithms?
Select the erie of tranformation that can move ΔABC onto ΔA'B'C'. A
Reflection over the line y=x. B
Reflection over the x-axi followed by a 90° clockwie rotation about the origin. C
Tranlation of (x12,y−4) followed rotation of 180o about the origin. D
Reflection over the x-axi followed by a tranlation (x12,y0)
The x and y coordinates switch places and are negated if you reflect over the line y = -x (the signs are changed). Point on the line y = x (y, x).
What is meant by Reflection?A reflection in mathematics is an isometric mapping from a Euclidean space to itself with a set of fixed points called the axis or plane of reflection. A figure's image created by a reflection is a mirror image of that figure in the axis or plane of reflection. A flip is the term for a reflection in geometry. The shape is mirrored in a reflection. The line of reflection is a line across which an image will reflect. Every point in a figure is said to reflect the other figure if and only if it is equally spaced from every corresponding point in the other figure.To learn more about Reflection, refer to:
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5. Find the sum. –10 + 1 + (–6) (1 point) –15 –17 –3 5
The simplified value of the expression - 10 + 1 + (- 6). - (15 - 17 - 35) is 20.
What is PEMDAS rule?PEMDAS rule states the correct order of simplifying an expression is as follows -: Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.
Given, An expression - 10 + 1 + (- 6). - (15 - 17 - 35).
Now, If any of the arithmetic operations are not present we'll simply do the next and we'll also distribute the negative and positive signs.
- 10 + 1 + (- 6). - (15 - 17 - 35).
= - 10 + 1 - 6 - 15 + 15 + 35.
= - 9 - 21 + 50.
= - 30 + 50.
= 20.
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What is a distribution that has both mean and median of (-15)?
A distribution that has both mean and median of (-15) is referred to as a perfectly symmetrical distribution.
What is a Perfectly symmetrical distribution?This is referred to as a type of distribution in which the values of the mean and the median are the same as they are the central component of inferential statistics.
In this scenario, we were given the mean and median to be of the same value which is (-15) which therefore denotes that the type of distribution is a perfectly symmetrical one.
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Can someone please help me with this? I don’t understand. Show work please.
Answer:
A
Step-by-step explanation:
angle 1+ angle 2 =180
so 2x-6+4x =180
6x =186
x =31
angle 1 = 2x-6 =31*2-6=62-6 = 56
angl2 =4x =31*4 =134
The heights of the bars of a histogram correspond to ______ values.
The heights of the bars of a histogram correspond to Frequency values.
A histogram is a type of graph used to show the distribution of a dataset. It is used to display the frequency of values within the data set by depicting the number of observations that fall within a set of ranges.
The heights of the bars of a histogram correspond to the frequency of values within the data set.
A histogram is used to illustrate the distribution of data within a set by showing the number of data points that fall within a specified range of values (called bins).
The height of each bar in the histogram represents the frequency of values within the bin range. A taller bar indicates that more data points fall within that range. The area of each bar is also proportional to the frequency of the values in the bin.
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